I need help with physics

We did a lab on simple harmonic motion with the pendulum. We made data tables for the time it takes for the pendulum to go back to its starting point, and he used different lengths of the string, and different masses, at different angles.
One of the questions on the lab is:

Given what you observed in this experiment, write a set of rules for constructing a pendulum clock that is reliable under a variety of temperatures.

What? I am using a string here. what does temperature have to do with anything.
I found out that in the clocks that uses pendulums, as the temp got higher, the length got longer. BUt I thought that didnt make a different. I dont know. Any one have thoughts? thanks.

If the length of the pedulum gets longer, the period will get longer. Also, as temperature increases, the air becomes less dense, so there is less air resistance, but that would hardly make a difference either. So I don't know what that's all about. But basically, I'd pick something with a long pendulum and a dense, heavy mass. This would have a low velocity, reducing air resistance, the heavy mass would minimize any inertia effects from the string, and rotational friction from the pivot would have a relatively very small torque.

If the length of the pedulum gets longer, the period will get longer. Also, as temperature increases, the air becomes less dense, so there is less air resistance, but that would hardly make a difference either. So I don't know what that's all about. But basically, I'd pick something with a long pendulum and a dense, heavy mass. This would have a low velocity, reducing air resistance, the heavy mass would minimize any inertia effects from the string, and rotational friction from the pivot would have a relatively very small torque.

Using Newton’s laws, we could show that for some pendulums...Does one of your graphs support this relationship? Explain. (Hint: Can the term in parentheses be treated as a constant of proportionality?)

-when we copied the lab at school to an e-mail it didnt have the equations. Here is my graph I quickly made (my other partner has the legitimate one):

Is the arm of the pendulum some material that expands or contracts due to heat? Aluminum will expand quite a bit in heat. Or if this was on a hot humid summer day and the arm was wood, that would expand as well. Right there your torque increases